PFR-declarations/PFR.ForMathlib.FiniteMeasureComponent.jsonl

{"name":"continuous_finiteMeasure_apply_of_isClopen","declaration":"/-- The measure of any connected component depends continuously on the `FiniteMeasure`. -/\ntheorem continuous_finiteMeasure_apply_of_isClopen {α : Type u_1} [TopologicalSpace α] [MeasurableSpace α] [OpensMeasurableSpace α] {s : Set α} (s_clopen : IsClopen s) : Continuous fun μ => (↑μ).real s"}
{"name":"continuous_probabilityMeasure_apply_of_isClopen","declaration":"/-- The probability of any connected component depends continuously on the `ProbabilityMeasure`. -/\ntheorem continuous_probabilityMeasure_apply_of_isClopen {α : Type u_1} [TopologicalSpace α] [MeasurableSpace α] [OpensMeasurableSpace α] {s : Set α} (s_clopen : IsClopen s) : Continuous fun μ => (↑μ).real s"}